Dependent Probability

Front

What is dependent probability?

Back

Dependent probability refers to the probability of an event occurring based on the outcome of a previous event. In dependent events, the outcome of one event affects the outcome of another.

Front

What is the formula for calculating the probability of two dependent events?

Back

P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of event B occurring after event A has already occurred.

Front

If a bag contains 3 red and 2 blue marbles, what is the probability of drawing a red marble first and then a blue marble without replacement?

Back

P(red first) = 3/5; P(blue second | red first) = 2/4 = 1/2; Therefore, P(red, then blue) = (3/5) * (1/2) = 3/10.

Front

What does 'without replacement' mean in probability?

Back

'Without replacement' means that once an item is drawn from a set, it is not put back into the set before the next draw, affecting the probabilities of subsequent draws.

Front

Calculate the probability of drawing a pink Starburst followed by a yellow Starburst from a pack of 3 orange, 6 pink, 1 yellow, and 5 red Starbursts without replacement.

Back

P(pink first) = 6/15; P(yellow second | pink first) = 1/14; Therefore, P(pink, then yellow) = (6/15) * (1/14) = 1/35.

Front

What is the probability of drawing two purple marbles from a box containing 5 purple, 3 green, and 2 orange marbles without replacement?

Back

P(purple first) = 5/10; P(purple second | purple first) = 4/9; Therefore, P(both purple) = (5/10) * (4/9) = 2/9.

Front

In a jar with 4 white chips, 5 purple chips, and 1 black chip, what is the probability of drawing a white chip, then a purple chip, then a black chip without replacement?

Back

P(white first) = 4/10; P(purple second | white first) = 5/9; P(black third | white and purple drawn) = 1/8; Therefore, P(white, then purple, then black) = (4/10) * (5/9) * (1/8) = 1/36.

Front

What is the probability of drawing a 1 and then a 6 from a set of numbers without replacement?

Back

If there are 6 total numbers, P(1 first) = 1/6; P(6 second | 1 first) = 1/5; Therefore, P(1, then 6) = (1/6) * (1/5) = 1/30.

Front

What is the probability of drawing two 9s from a set of 8 numbers without replacement?

Back

If there are 2 nines in the set, P(9 first) = 2/8; P(9 second | 9 first) = 1/7; Therefore, P(9, then 9) = (2/8) * (1/7) = 1/28.

Front

What is the difference between independent and dependent events in probability?

Back

Independent events are those where the outcome of one event does not affect the outcome of another. Dependent events are those where the outcome of one event does affect the outcome of another.