A problem in mathematics is given to 3 students whose chances of solving individually are ½ , ⅓ and ¼. The probability that the problem will be solved at least by one, is what?
The best way to solve this is to first find the probability of them not been able to solve the question individually, then from that find the probability of them not been able to solve the question collectively. From there, you can then find the probability of one of them solving it (which will be 1 - probability of them not solving it).
Probability of them not been able to solve the question individually will be (1 - ½ ), (1 - ⅓) and (1 - ¼) Which are: ½, ⅔ and ¾
Probability of them not been able to solve the question collectively will then be: ½ x ⅔ x ¾ = ⁶⁄₂₄ ⁶⁄₂₄ can be reduced to ¼
The probability of then solving the question collectively will then be 1 - ¼ = ¾
A problem in mathematics is given to 3 students whose chances of solving individually are ½ , ⅓ and ¼. The probability that the problem will be solved at least by one, is what?
The best way to solve this is to first find the probability of them not been able to solve the question individually, then from that find the probability of them not been able to solve the question collectively. From there, you can then find the probability of one of them solving it (which will be 1 - probability of them not solving it).
Probability of them not been able to solve the question individually will be (1 - ½ ), (1 - ⅓) and (1 - ¼) Which are: ½, ⅔ and ¾
Probability of them not been able to solve the question collectively will then be: ½ x ⅔ x ¾ = ⁶⁄₂₄ ⁶⁄₂₄ can be reduced to ¼
The probability of then solving the question collectively will then be 1 - ¼ = ¾
Answer: ¾
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Spiking bond yields driving sharp losses in tech stocks
A spike in interest rates since the start of the year has accelerated a rotation out of high-growth technology stocks and into value stocks poised to benefit from a reopening of the economy. The Nasdaq has fallen more than 10% over the past month as the Dow has soared to record highs, with a spike in the 10-year US Treasury yield acting as the main catalyst. It recently surged to a cycle high of more than 1.60% after starting the year below 1%. But according to Jim Paulsen, the Leuthold Group's chief investment strategist, rising interest rates do not represent a long-term threat to the stock market. Paulsen expects the 10-year yield to cross 2% by the end of the year.
A spike in interest rates and its impact on the stock market depends on the economic backdrop, according to Paulsen. Rising interest rates amid a strengthening economy "may prove no challenge at all for stocks," Paulsen said.
Traders also expressed uncertainty about the situation with China Evergrande, as the indebted property company has not provided clarification about a key interest payment.In economic news, the Commerce Department reported an unexpected increase in U.S. new home sales in August.Crude oil prices climbed Friday and front-month WTI oil futures contracts saw gains for a fifth straight week amid tighter supplies. West Texas Intermediate Crude oil futures for November rose $0.68 or 0.9 percent at 73.98 a barrel. WTI Crude futures gained 2.8 percent for the week.
