Question

# Taylor has a set of 32 cards. There are 16 yellow cards and 16 brown cards in the set. The first 6 cards that Taylor draws are yellow, brown, yellow, yellow, yellow, and brown. Based on these results, what is the probability that the next card he draws will be yellow?

Probability and combinatorics
Taylor has a set of 32 cards. There are 16 yellow cards and 16 brown cards in the set. The first 6 cards that Taylor draws are yellow, brown, yellow, yellow, yellow, and brown. Based on these results, what is the probability that the next card he draws will be yellow?

2020-11-02

Given:
32 cards in total
16 yellow cards
16 brown cards
First 6 drawn cards: yellow, brown, yellow, yellow, brown
Since 6 of the 32 cards were already drawn, there are $$32-6=26$$ cards remaining.
# of possible outcomes $$= 26$$
The set of cards contains 16 yellow cards, while 4 of the yellow cards were already drawn and thus there are $$16-4=12$$ yellow cards remaining that we can select on the next draw:
# of favorable outcomes $$= 12$$
The probability is the number of favorable outcomes divided by the number of possible outcomes
P(Next card is yellow)= # of favorable outcomes # of possible outcomes=$$\displaystyle\frac{{12}}{{26}}=\frac{{6}}{{13}}\sim{0.4615}={46.15}\%$$