Complete question :
Elena loves to go fishing. Each time she catches a fish, there is a 70, percent chance that it is a northern pike and a 30, percent chance it is a walleye. Let X be the random variable that represents the number of northern pike Elena gets if she catches 2 fish. Find the expected value of the number of Northern pikes Elena catches
Answer: 1.4
Explanation:
P(Northern pike) = 0.7
P(walleye) = 0.3
If 2 fishes are caught :
Number of northern pike (x) :
X = 0
P(walleye 1 st) * p(walleye 2nd) = (0.3 * 0.3) = 0.09
X = 1
P(walleye 1st)*P(Northern pike 2nd) OR P(Northern pike 1st)*P(Walleye 2nd)
= (0.3 * 0.7) + (0.7 * 0.3)
= 0.21 + 0.21
= 0.42
P(x = 2)
P(northern pike 1st) * P(northen pike 2nd)
0.7 *0.7 = 0.49
X: ______ 0 _____ 1 _______ 2
P(x): ___ 0.09 ___ 0.42 ____ 0.49
Expected value of northern pikes :
(0* 0.09) + (1 * 0.42) + (2 * 0.49)
0 + 0.42 + 0.98
= 1.4