Of the 7 males and 5 females, there are two sets of siblings. One set consists of a brother and sister, and the other set consists of a brother and his 2 sisters. The lead roles are cast randomly.
B. What is the probability that a pair of siblings are cast in the lead roles?
I don't get this probability question.
wouldn't you have to add the 2 # s so it'll be 1/12 too??
missing information.
In what way are the sibling choices affecting the casting?
e.g. can the 2 siblings not be cast together?
I'm still not understanding what you mean. So the siblings can be casted together because there are 7 males and 5 females and 2 sets of siblings could potentially have those roles.So how should I write the probability?
ok, I misread your question
total number of castings = 35
number of casting with the one brother and sister = 1
number of castings with the one brother and two sisters = 1 x 2 = 2
prob (bother and sister in casting) = 3/35
To understand this probability question, we need to consider the number of possible pairs of siblings that can be cast in the lead roles out of the total number of possible combinations. Let's break it down step by step:
Step 1: Determine the number of males and females available. The question states that there are 7 males and 5 females in total.
Step 2: Identify the two sets of siblings. One set consists of a brother and sister, and the other set consists of a brother and his 2 sisters.
Step 3: Calculate the total number of ways the lead roles can be cast. Since the roles are cast randomly, any male can be cast in a male lead role and any female can be cast in a female lead role. Thus, the total number of ways the lead roles can be cast is the product of the number of males and the number of females, which is 7 * 5 = 35.
Step 4: Count the number of possible pairs of siblings. In this case, there are two possible pairs: the brother and sister, and the brother and his 2 sisters.
Step 5: Calculate the probability. The probability is the number of ways the desired event can occur (siblings being cast in the lead roles) divided by the total number of possible outcomes (all possible combinations of casting the lead roles). In this case, the number of ways the desired event can occur is 2 (the number of possible sibling pairs), and the total number of possible outcomes is 35. Therefore, the probability is 2/35.
So, the probability that a pair of siblings are cast in the lead roles is 2/35, not 1/12.
It's important to note that when calculating probabilities, it's necessary to consider all the given information and conditions stated in the problem and determine the total number of possible outcomes and the number of desired outcomes within those possibilities.