Question

You draw a card at random from a deck that contains 333 black cards and 777 red cards. What is \text{P(draw a black card})P(draw a black card)start text, P, left parenthesis, d, r, a, w, space, a, space, b, l, a, c, k, space, c, a, r, d, end text, right parenthesis? If necessary, round your answer to 222 decimal places.

Answer 1

0.435 Got it from Khan

Explanation:

Hint #11 / 3

All of the probabilities in a valid probability distribution must add up to 111.

Hint #22 / 3

Solve for the missing probability:

\begin{aligned} 0.475+\text{?}+0.090&=1 \\\\ 0.565+\text{?}&=1 \\\\ \text{?}&=0.435 \end{aligned}

0.475+?+0.090

0.565+?

?

​

=1

=1

=0.435

​

Hint #33 / 3

The answer:

P\left(Y=1\right)=0.435P(Y=1)=0.435

Answer 2

The probability of picking a black card at random, from a deck with 3 black cards and 7 red ones is 0.3.

Explanation:

We will assume that we have 3 black cards and 7 black cards, for a total of 10 cards. Since we are taking one card at random, we can assume that each card is equally likely to be drawn. We have the following event A: The drawn card is a black. We will find the probability of A as counting the number of outcomes that make A to occur and divide it by the total number of possibilities. We are drawing one card, so we have 10 possibilities to be picked. Out of those 10, only 3 cards are black, hence we have 3 possibilites of picking a black card.

Then,

P(A) = 3/10 = 0.3.