A jar contains 7 black balls and 25 red balls. You take 2 out without replacing them. Find a)the probability of drawing 2 red balls in a row, b) the probability of

drawing a red ball, then a black ball,
c) the probability that the two balls will be of different colors

a) prob = (25/32)(24/31) = ..

b) prob = (25/32)(7/31) = ...

c) prob (both red) = answer to a)
prob(both black) = (7/32)(6/31) = ..

prob(different colour) = 1 - a) - both black

To solve these probability problems, we need to first understand the total number of balls and the number of each color. In this case, there are 7 black balls and 25 red balls, making a total of 32 balls.

a) The probability of drawing 2 red balls in a row:
When we draw the first ball, there are 32 balls in the jar, and 25 of them are red. So, the probability of drawing a red ball on the first try is 25/32. After drawing a red ball, there are now 31 balls in the jar, and 24 of them are red. So, the probability of drawing a second red ball is 24/31. To find the probability of both events happening, we multiply the individual probabilities: (25/32) * (24/31) ≈ 0.466.

b) The probability of drawing a red ball, then a black ball:
Similarly, the probability of drawing a red ball on the first try is 25/32. After drawing a red ball, there are 31 balls left in the jar, but the number of black balls remains the same (7). Therefore, the probability of drawing a black ball on the second try is 7/31. To find the overall probability, we multiply the individual probabilities: (25/32) * (7/31) ≈ 0.151.

c) The probability that the two balls will be of different colors:
To calculate this probability, we need to find the probability of drawing a red ball, then a black ball, and add it to the probability of drawing a black ball, then a red ball. Using the same logic as before, the probability of drawing a red ball, then a black ball is (25/32) * (7/31) ≈ 0.151. Conversely, the probability of drawing a black ball, then a red ball is (7/32) * (25/31) ≈ 0.071. Finally, adding these two probabilities together gives us the total probability of (0.151 + 0.071) ≈ 0.222.

Therefore, the answers to the questions are:
a) The probability of drawing 2 red balls in a row is approximately 0.466.
b) The probability of drawing a red ball, then a black ball is approximately 0.151.
c) The probability that the two balls will be of different colors is approximately 0.222.