cybil flips a coin and rolls a fair number cube at the same time. What is the probability that she will toss tails and roll a nu
1 answer:
Answer:
Step-by-step explanation:
Flipping a coin and rolling a number cube are both independent events. Independent events do not rely on the outcome of any previous events. This means that whatever you flip on the coin will have no effect on whatever you roll on the number cube and each flip of the coin or roll of the cube has the same probability as the flip or roll before.
The probability of getting tails on a coin toss is:
The probability of getting a number less than 3 (so 1 or 2) on a number cube is:
Since we are combining these events, we need to multiply the fractions together to get our overall probability:
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Answer:
Step-by-step explanation:
We need to find the value of
Solving:
We know,
a^0 = 1
so,
So, the value of
Answer:
(a) The probability that a text message user receives or sends three messages per hour is 0.2180.
(b) The probability that a text message user receives or sends more than three messages per hour is 0.2667.
Step-by-step explanation:
Let <em>X</em> = number of text messages receive or send in an hour.
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em>.
It is provided that users receive or send 62.7 text messages in 24 hours.
Then the average number of text messages received or sent in an hour is: .
The probability of a random variable can be computed using the formula:
(a)
Compute the probability that a text message user receives or sends three messages per hour as follows:
Thus, the probability that a text message user receives or sends three messages per hour is 0.2180.
(b)
Compute the probability that a text message user receives or sends more than three messages per hour as follows:
P (X > 3) = 1 - P (X ≤ 3)
= 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)
Thus, the probability that a text message user receives or sends more than three messages per hour is 0.2667.