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3 years ago

What is the least common denominator 2 and 7?

Mathematics

2 answers:

natima [27]3 years ago

8 0

Answer:

Step-by-step explanation:

Ostrovityanka [42]3 years ago

4 0

14 7x2=14 please give Brain

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3 years ago

fair coin is tossed three times. What is the probability that all three tosses land on heads,given that:(a) the first toss lands

maxonik [38]

Answer:

(a) The probability that all three tosses land on heads given that the 1st toss lands on Heads is $\frac{1}{4}$ .

(b) The probability that all three tosses land on heads given that at least one toss lands on heads is $\frac{1}{7}$ .

Step-by-step explanation:

The sample space of tossing 3 coins is:

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} = 8 outcomes.

(a)

The sample space such that the 1st toss lands on Heads is:

S₁ = {HHH, HHT, HTH, HTT} = 4 outcomes.

The probability that all three tosses land on heads given that the 1st toss lands on Heads is:

P (3 Heads | 1st toss is Heads) = $\frac{P(3\ Heads\ \cap \ 1st\ toss\ is\ Heads)}{P(1st\ toss\ is\ Heads)}$

$=\frac{\frac{1}{4} }{\frac{4}{8} } \\=\frac{1}{8}\times \frac{8}{4}\\ =\frac{1}{4}$

Thus, the probability that all three tosses land on heads given that the 1st toss lands on Heads is $\frac{1}{4}$ .

(b)

The sample space such that at least one toss lands on heads is:

S₂ = {HHH, HHT, HTH, THH, HTT, THT, TTH} = 7 outcomes

The probability that all three tosses land on heads given that at least one toss lands on heads is,

P (3 Heads | At least 1 Heads) $=\frac{P(3\ Heads\ \cap\ At\ least\ 1\ Heads)}{P( At\ least\ 1\ Heads)}$

$=\frac{\frac{1}{7} }{\frac{7}{8} } \\=\frac{1}{8}\times \frac{8}{7}\\ =\frac{1}{7}$

Thus, the probability that all three tosses land on heads given that at least one toss lands on heads is $\frac{1}{7}$ .

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3 years ago