Answer: The answer is (b) a ≤ 3 + 2j; j ≥ 14, a ≤ 35.
Step-by-step explanation: Given that Anna is no more than 3 years older than 2 times Jamie’s age. Jamie is at least 14 and Anna is at most 35. We are to select the correct combination of inequalities among the given options.
Also, 'a' and 'j' are the possible ages of Anna and Jamie respectively. Therefore, according to the given information, we can write
Thus, the correct option is (b) a ≤ 3 + 2j; j ≥ 14, a ≤ 35.
Answer:
The probabilities of each outcome are the following:
for X = 1 is 0.6
for X = 2 is 0.35
for X = 3 is 0.049
and for X = 4 is 0.001
Step-by-step explanation:
Let's consider X as the random variable for the sum of outcomes "S" exceeds 3, this is:
Let's now analyze and consider the ways that X equals the different values:
X = 1: I throw the dice and the result is: 4, 5 and 6.
Then: P(X=1) = P(4) + P(5) + P(6) = 0.2+0.1+0.3 = 0.6
Thus P(X=1) = 0.6
X = 2: The result after following the dice two times can be:
1 and 3, 1 an 4.... and so on until 1 and 6
2 and 2, 2 and 3... and so on until 2 and 6
3 and 1... and so on until 3 a 6
Then P(X=2) = P(1)xP(3,4,5,6) + P(2)xP(2....6) + P(3)x(1.....6)
Theory of Probability: Sum of all possible outcomes P(1)+P(2).......P(6) = 1
Then P(1......6) = 1
Then P(X=2) = P(1)x[1-P(1)-P(2)]+P(2)x[1-P(1)]+P(3) = 0.1x(1-0.1-0.2) + 0.2x(1-0.1) + 0.1 = 0.1 x 0.7 + 0.2 x 0.9 + 0.1 = 0.35
Thus P(X=2) = 0.35
X = 3: The result can be
1 and 1 and 2, 1 and 1 and 3.... until 1 and 1 and 6
1 and 2 and 1, 1 and 2 and 2..... until 1 and 2 and 6
2 and 1 and 1, 2 and 1 and 2.... until 2 and 1 and 6
Then P(X=3) = P(1)xP(1)xP(2....6) + P(1)xP(2)xP(1.....6) + P(1)xP(2)xP(1.....6)
P(X=3) = 0.1 x 0.1 x (1-0.1) + 0.1 x 0.2 x 1 + 0.2 x 0.1 x 1 = 0.01 x 0.9 + 0.2 + 0.2 = 0.049
Thus P(X=3) = 0.049
Finally, for X to be 4, I only have the following possibilities
1 and 1 and 1 and 1.... until 1 and 1 and 1 and 6
Then P(X=4) = P(1)xP(1)xP(1)xP(1.....6) = 0.1x0.1x0.1x1 = 0.001
Thus P(X=3) = 0.001