Question

Probability that missing card is not a spade, given two drawn cards are spades?

• A. $\frac{3}{50}$
• B. $\frac{39}{50}$
• C. $\frac{39}{52}$
• D. $\frac{38}{52}$

Hint:

Bayes’ Theorem. Update prior probabilities using evidence from observed events.

Answer 1

The Correct Option is B

Use Bayes’ theorem with two cases: missing card is spade or not. \[ P(E|M_S) = \frac{66}{1275},\quad P(E|M_{NS}) = \frac{78}{1275} \] \[ P(M_{NS}|E) = \frac{78 \cdot 39}{78 \cdot 39 + 66 \cdot 13} = \frac{39}{50} \]