Question

You are certain to get 3 jacks when selecting 51 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

Answer 1

Answer:

0.001145

Step-by-step explanation:

Given that you are certain to get 3 jacks when selecting 51 cards from a shuffled deck.

When we draw 3 cards from 51 cards, we keep one card aside

The card can be either Jack or non Jack

Prob (the left over card to be Jack) = P(A) = $\frac{4}{52}$

Prob (the left over card to be non jack ) = P(B) = $\frac{48}{52}$

A and B are mutually exclusive and exhaustive

Let drawing 3 Jacks be the event C

P(C) = P(AC)+P(BC)

$P(AC) = P(A)*P(C/A)\\= \frac{4}{52} (3/51C3)\\=1.108(10^{-5}$

P(BC) = P(B)*P(C/B)\\

= \frac{28}{52} (4/51C3)\\

=1.034(10^{-4}

Adding we get

P(C)

= $(1.108+10.343)(10^{-5} \\=0.001145$