Respuesta :
Answer:
The probability that at least one of the stocks will rise in price is 0.70.
Step-by-step explanation:
The conditional probability of event X given that another event Y has already occurred is:
[tex]P(X|Y)=\frac{P(X\cap Y)}{P(Y)}[/tex]
Denote the events as follows:
A = stock A rises in price
B = stock B rises in price
Given:
P (A) = 0.40
P (B) = 0.50
P (A|B) = 0.50
Compute the value of P (A ∩ B) as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}\\P(A\cap B)=P(A|B)P(B)\\=0.50\times0.60\\=0.30[/tex]
The probability that at least one of the stock rises is same as the probability of either stock A or B rising.
Compute the value of P (A ∪ B) as follows:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\=0.40+0.60-0.30\\=0.70[/tex]
Thus, the probability that at least one of the stocks will rise in price is 0.70.
The probability that at least one of the stocks will rise in price is [tex]0.7[/tex].
Conditional Probability:
It is the probability of event A given that another event B has already occurred is,
[tex]P(A/B)=\frac{P(A\cap B)}{P(B)}[/tex]
Where,
- A represent stock A rises in price
- B represent stock B rises in price
Given that,[tex]P (A) = 0.40, P (B) = 0.50, P (A|B) = 0.50[/tex]
Compute the value of [tex]P (A \cap B)[/tex] shown below,
[tex]P(A\cap B)=0.5*0.6=0.3[/tex]
The probability that at least one of the stocks will rise in price is,
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\P(A\cup B)=0.4+0.6-0.3=0.7[/tex]
Learn more about the probability here:
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