A bag soccer balls contains 8 balls with black design and 7 balls with red design with no other types of soccer balls. Coach graves reaches into the bag and randomly pulls out two soccer balls.
please check my answer
a) explain these events are either dependent or independent.
i think this is independent because the coach just randomly chooses the ball.
b) what is the propability both of the balls will be the ame design color?
is it 98/15.....
Since probability is a value between zero and 1, you should have realized immediately that your answer made no sense.
prob of 2 black balls = 8/15 * 7/14 = 56/210
prob of 2 red balls = 7/15 * 6/15 = 42/210
so the prob of either 2 black OR 2 red balls = 98/210 = 7/15
(notice that the only other possibility would have been to have a black and then a red which would be
2(8/15 / 7/14) = 8/15
and 7/15 + 8/15 = 1 )
a) You are correct, the events of pulling out the soccer balls are independent. This is because the coach randomly chooses the balls from the bag without any influence or preference.
b) To calculate the probability of both balls being the same color, we need to consider two scenarios: both balls are black or both balls are red.
1. Probability of drawing two black balls:
The probability of drawing the first black ball from the bag is 8/15 (since there are 8 black balls out of a total of 15 balls in the bag). After removing one black ball, there are now 7 black balls left out of 14 balls in the bag. Therefore, the probability of drawing a second black ball is 7/14. To find the probability of both events occurring together, we multiply the individual probabilities: (8/15) * (7/14) = 56/210.
2. Probability of drawing two red balls:
The probability of drawing the first red ball from the bag is 7/15 (since there are 7 red balls out of a total of 15 balls in the bag). After removing one red ball, there are now 6 red balls left out of 14 balls in the bag. Therefore, the probability of drawing a second red ball is 6/14. To find the probability of both events occurring together, we multiply the individual probabilities: (7/15) * (6/14) = 42/210.
To find the probability of both balls being the same color (either both black or both red), we add the probabilities from both scenarios: (56/210) + (42/210) = 98/210.
Simplifying 98/210 by dividing both numerator and denominator by 14 (which is the greatest common divisor) gives us the simplified form of the probability: 7/15.
Therefore, the correct probability of both balls being the same color is 7/15, not 98/15.