Probability of Independent and Dependent Events

Front

What is the definition of independent events in probability?

Back

Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other event(s).

Front

What is the definition of dependent events in probability?

Back

Dependent events are two or more events where the occurrence of one event affects the occurrence of the other event(s).

Front

How do you calculate the probability of two independent events occurring together?

Back

The probability of two independent events A and B occurring together is calculated by multiplying their individual probabilities: P(A and B) = P(A) * P(B).

Front

How do you calculate the probability of two dependent events occurring together?

Back

The probability of two dependent events A and B occurring together is calculated by multiplying the probability of the first event by the conditional probability of the second event given the first: P(A and B) = P(A) * P(B|A).

Front

What is the probability of drawing two purple pencils from a basket containing 5 purple and 9 brown pencils without replacement?

Back

The probability is calculated as follows: P(first purple) = 5/14, P(second purple | first purple) = 4/13. Therefore, P(both purple) = (5/14) * (4/13) = 20/182 = 10/91.

Front

What is the probability of selecting a purple chip followed by a black chip from a jar containing 4 white, 5 purple, and 1 black chip without replacement?

Back

The probability is calculated as follows: P(purple) = 5/10, P(black | purple) = 1/9. Therefore, P(purple then black) = (5/10) * (1/9) = 5/90 = 1/18.

Front

How does replacement affect the probability of selecting letters from a word?

Back

If the first letter is replaced, the total number of letters remains the same for the second selection, making the events independent. If not replaced, the total number of letters decreases, making the events dependent.

Front

What is the probability of selecting an 'N' first and a 'D' next from the word 'UNDERSTAND' with replacement?

Back

The probability is calculated as follows: P(N) = 2/10, P(D) = 1/10. Therefore, P(N then D) = (2/10) * (1/10) = 2/100 = 1/50.

Front

What is the probability of picking two red marbles from a bag containing 6 red, 5 green, and 4 yellow marbles without replacement?

Back

The probability is calculated as follows: P(first red) = 6/15, P(second red | first red) = 5/14. Therefore, P(both red) = (6/15) * (5/14) = 30/210 = 1/7.

Front

What is the probability of selecting a gumball followed by a lollipop from a treat bag containing 6 lollipops and 4 gum balls without replacement?

Back

The probability is calculated as follows: P(gumball) = 4/10, P(lollipop | gumball) = 6/9. Therefore, P(gumball then lollipop) = (4/10) * (6/9) = 24/90 = 4/15.