Reproductive Health Set-5

Q1. A couple has unprotected intercourse once during a woman's 28‑day menstrual cycle; the day of intercourse is equally likely to be any day from 1 to 28. If ovulation occurs on day 14, sperm can survive up to 5 days in the female reproductive tract and the ovum is viable for 24 hours, what is the probability that this single intercourse results in conception in that cycle?

Q2. In an IVF cycle 12 mature oocytes are retrieved. For each oocyte: probability of fertilization is 70%; if fertilized, probability of reaching day‑3 embryo is 60%; probability that a day‑3 embryo becomes a blastocyst is 50%; probability that a transferred blastocyst implants is 40%. Assuming independent outcomes for each oocyte, the probability that at least one embryo implants from this cycle is:

Q3. Both parents are known carriers of an autosomal recessive disorder. The prior probability that a fetus is affected is $1/4$. A prenatal diagnostic test (amniocentesis) for the disorder has sensitivity $98\%$ and specificity $99\%$. If the test result is positive for "affected", the posterior probability that the fetus is truly affected is closest to:

Q4. Assertion (A): Vasectomy and tubectomy are both highly effective permanent sterilization procedures; neither procedure significantly alters sex‑steroid (testosterone/estrogen) production in the individual.
Reason (R): Both procedures render the individual sterile by interrupting the blood supply to the gonads, thereby stopping gametogenesis.

Q5. In a seropositive male-to-female HIV scenario the per‑act transmission probability without a condom is $p=0.01$ (1%). Condoms, when used, reduce per‑act transmission by 90% (residual risk $0.1p$ per protected act). A couple had 100 sexual acts in a year: condoms were used in 90 acts and not used in 10 acts. Assuming independence of acts, the probability that the woman acquires infection at least once during the year is approximately:

Q6. In a clinical study 200 women used a contraceptive method X continuously for one year and 3 pregnancies occurred during that year. Using the Pearl Index defined as $\displaystyle \text{Pearl Index}=\frac{\text{number of pregnancies}\times 100}{\text{total woman‑years}}$, calculate the Pearl Index (per 100 woman‑years) for method X.

Q7. A couple seeks fertility treatment. The female partner has bilateral distal tubal blockage on hysterosalpingography and the male partner has severe oligospermia with total motile sperm count ≈ 2 million. Which assisted reproductive technique is most appropriate for them?

Q8. A woman uses contraceptive A with a typical-use failure rate of $2\%$ per year for 3 years, then switches to contraceptive B with failure rate $12\%$ per year for 2 years. Assuming each year's failure events are independent and rates are constant, the probability that she avoids pregnancy over the entire 5‑year period is

Q9. Assertion (A): Levonorgestrel emergency contraceptive pills taken within 72 hours after unprotected intercourse primarily prevent pregnancy by inhibiting or delaying ovulation.
Reason (R): Because levonorgestrel chiefly acts after fertilization by preventing implantation, it remains equally effective if taken up to 5 days after intercourse.
Which of the following is correct?

Q10. In a population with Chlamydia trachomatis prevalence $5\%$, a screening test has sensitivity $90\%$ and specificity $95\%$. Using Bayes' theorem and the formula $\displaystyle \text{PPV}=\frac{\text{sensitivity}\times\text{prevalence}}{\text{sensitivity}\times\text{prevalence}+(1-\text{specificity})\times(1-\text{prevalence})}$, the positive predictive value (PPV) of a positive test result is approximately:

Q11. A couple uses a barrier method with efficacy $0.90$ (90%) and a spermicide with efficacy $0.85$ (85%) during a single act of intercourse. Assuming independent mechanisms, the probability of pregnancy in that act is

Q12. In a woman with a regular 28‑day cycle who has unprotected intercourse on day 12, an emergency contraceptive pill containing levonorgestrel is taken $48$ hours later (day $14$). Considering the primary mechanism of levonorgestrel, which statement is most accurate?

Q13. A couple seeks assisted reproduction. Investigations show: female—bilateral tubal blockage on hysterosalpingography; male—semen analysis: sperm concentration $12\times10^{6}\,\text{mL}^{-1}$ and progressive motility $20\%$. Considering both partners' findings, the MOST appropriate assisted reproductive technique is

Q14. Assertion (A): A woman taking combined oral contraceptives (COCs) who is prescribed rifampicin for tuberculosis is at increased risk of contraceptive failure.
Reason (R): Rifampicin is a potent inducer of hepatic cytochrome P450 enzymes which accelerates metabolism and clearance of steroid hormones in COCs, lowering their plasma concentration and reducing contraceptive efficacy.

Q15. In an IVF cycle three embryos are transferred and each embryo independently has probability $p=0.20$ of successful implantation. The probability that the cycle results in a twin pregnancy (exactly two embryos implanting) is