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Answer:
a) 0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.
b) probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
A) Find the probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.
Two from the best friend:
Her best friend sends a message once every 10 minutes.
From 6 to 7:30, there is an hour and a half, that is, 90 minutes, so the mean for her best friend is
Two messages is P(X = 2). So
Two from the mother:
Message every hour = 60 minutes. So . This is P(X = 2).
Two of her best friend and two of her mother:
Independent events, so the probability of both happening is the multiplication of their separate probabilities.
0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.
B) With a chance of 75% a text message contains a typo independent of the sender. Find the probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.
In 3 hours, she is expected to receive:
3*60/10 = 18 messages from her best friend.
3*60/60 = 3 messages from her mother.
3*60/30 = 6 messages from her brother.
In total, 27 messages.
75% probability of a typo, so
This is P(X = 0).
probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.