Thread: Probability

A and B take it in turns, starting with A, to take a card, without replacement, from a pack of 10 cards containing the numbers 1,2,2,3,3,3,4,4,4,4.

The first player to select a "4" card is the winner.

Find the probability that B wins the game.

Hello, BabyMilo!

Starting with , players and take turns taking a card, without replacement,
from a pack of 10 cards marked: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4.

The first player to select a "4" card is the winner.

Find the probability that wins the game.

There are: 4 Fours and 6 Others.

A tree diagram makes the problem clear.

There are three scenarios in which wins.


[1] draws an Other, then draws a Four.
. . .This probability is: .

[2] draws an Other, draws an Other,
. . . draws an Other, then draws a Four.
. . .This probability is: .

[3] draws an Other, draws an Other,
. . . draws an Other, draws an Other,
. . . draws an Other, then draws a Four.
. . .This probability is: .


Therefore: .

But check my work . . . please!
.