sameena has round pencil case and a square pencil case there are 4 blue pens and 3 red pens in round pencil case there are 4 blue pens and 5 red pens in square pencil case work out the probability that pens sameena taken are both red solution
To work out the probability that Sameena takes out two red pens, we need to find the probability of selecting a red pen from each pencil case and multiply the probabilities together.
Let's label the events:
A: Selecting a red pen from the round pencil case.
B: Selecting a red pen from the square pencil case.
The probability of selecting a red pen from the round pencil case is given as 3 red pens out of a total of 7 pens (4 blue + 3 red) in the round pencil case:
P(A) = 3/7
The probability of selecting a red pen from the square pencil case is given as 5 red pens out of a total of 9 pens (4 blue + 5 red) in the square pencil case:
P(B) = 5/9
Now we can calculate the probability of both events occurring by multiplying the individual probabilities:
P(A and B) = P(A) * P(B)
= (3/7) * (5/9)
= 15/63
= 5/21
Therefore, the probability that Sameena takes out two red pens is 5/21.
To work out the probability that the pens Sameena has taken are both red, we need to find the number of favorable outcomes (both red pens) and the total number of possible outcomes.
First, let's calculate the favorable outcomes:
- Sameena has a round pencil case with 3 red pens.
- Sameena also has a square pencil case with 5 red pens.
To find the probability that both pens are red, we need to multiply the probabilities of choosing a red pen from each case. Since the events (choosing from round pencil case and square pencil case) are independent, we can multiply the probabilities together.
Probability of choosing a red pen from the round pencil case:
= Number of red pens in the round pencil case / Total number of pens in the round pencil case
= 3 red pens / (4 blue pens + 3 red pens)
= 3/7
Probability of choosing a red pen from the square pencil case:
= Number of red pens in the square pencil case / Total number of pens in the square pencil case
= 5 red pens / (4 blue pens + 5 red pens)
= 5/9
To find the probability of choosing both pens as red, we multiply the probabilities together:
= (3/7) * (5/9)
= 15/63
However, we can simplify the probability by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
= (15/3) / (63/3)
= 5/21
Therefore, the probability that Sameena has taken both red pens is 5/21.
What is
(3/7)(5/9) ?