of a set of 10 cards, 3 have red circles, 4 have yellow triangles, and 3 have green diamonds. you choose one card at random and then replace it. then you choose a second card. what is the probability that both cards have yellow triangles?
Find the probability of obtaining the first card. Since you are replacing the card, that is the same as the probability of obtaining the second card. The probability of all events occurring is obtained by multiplying the probabilities of the individual events.
I hope this helps. Thanks for asking.
To find the probability that both cards have yellow triangles, we need to calculate the probability of drawing a yellow triangle on the first card and then drawing a yellow triangle again on the second card.
Step 1: Calculate the probability of drawing a yellow triangle on the first card.
Out of the 10 cards, 4 have yellow triangles.
So, the probability of drawing a yellow triangle on the first card is 4/10 or 2/5.
Step 2: Since the first card is replaced, the deck remains the same and the probability of drawing a yellow triangle on the second card is still 4/10 or 2/5.
Step 3: Calculate the probability of both events occurring by multiplying the individual probabilities.
P(both cards have yellow triangles) = P(first card is yellow triangle) * P(second card is yellow triangle)
P(both cards have yellow triangles) = (2/5) * (2/5)
P(both cards have yellow triangles) = 4/25
Therefore, the probability that both cards drawn have yellow triangles is 4/25 or 0.16.